Nektar++
BetaPressureArea.cpp
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1///////////////////////////////////////////////////////////////////////////////
2//
3// File: BetaPressureArea.cpp
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7// The MIT License
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9// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
10// Department of Aeronautics, Imperial College London (UK), and Scientific
11// Computing and Imaging Institute, University of Utah (USA).
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31//
32// Description: BetaPressureArea class
33//
34///////////////////////////////////////////////////////////////////////////////
35
36#include <PulseWaveSolver/EquationSystems/BetaPressureArea.h>
37
38namespace Nektar
39{
40
41std::string BetaPressureArea::className =
42 GetPressureAreaFactory().RegisterCreatorFunction(
43 "Beta", BetaPressureArea::create,
44 "Beta law pressure area relationship for the arterial system");
45
46BetaPressureArea::BetaPressureArea(
47 Array<OneD, MultiRegions::ExpListSharedPtr> pVessel,
48 const LibUtilities::SessionReaderSharedPtr pSession)
49 : PulseWavePressureArea(pVessel, pSession)
50{
51}
52
53void BetaPressureArea::v_GetPressure(NekDouble &P, const NekDouble &beta,
54 const NekDouble &A, const NekDouble &A0,
55 const NekDouble &dAUdx,
56 const NekDouble &gamma,
57 [[maybe_unused]] const NekDouble &alpha)
58{
59 P = m_PExt + beta * (sqrt(A) - sqrt(A0)) -
60 gamma * dAUdx / sqrt(A); // Viscoelasticity
61}
62
63void BetaPressureArea::v_GetC(NekDouble &c, const NekDouble &beta,
64 const NekDouble &A,
65 [[maybe_unused]] const NekDouble &A0,
66 [[maybe_unused]] const NekDouble &alpha)
67{
68 c = sqrt(beta / (2 * m_rho)) * sqrt(sqrt(A)); // Elastic
69}
70
71void BetaPressureArea::v_GetW1(NekDouble &W1, const NekDouble &u,
72 const NekDouble &beta, const NekDouble &A,
73 const NekDouble &A0,
74 [[maybe_unused]] const NekDouble &alpha)
75{
76 NekDouble I = 0.0;
77 GetCharIntegral(I, beta, A, A0);
78
79 W1 = u + I; // Elastic and assumes u0 = 0
80}
81
82void BetaPressureArea::v_GetW2(NekDouble &W2, const NekDouble &u,
83 const NekDouble &beta, const NekDouble &A,
84 const NekDouble &A0,
85 [[maybe_unused]] const NekDouble &alpha)
86{
87 NekDouble I = 0.0;
88 GetCharIntegral(I, beta, A, A0);
89
90 W2 = u - I; // Elastic and assumes u0 = 0
91}
92
93void BetaPressureArea::v_GetAFromChars(NekDouble &A, const NekDouble &W1,
94 const NekDouble &W2,
95 const NekDouble &beta,
96 const NekDouble &A0,
97 [[maybe_unused]] const NekDouble &alpha)
98{
99 A = pow((W1 - W2) * sqrt(2 * m_rho / beta) / 8 + sqrt(sqrt(A0)), 4);
100}
101
102void BetaPressureArea::v_GetUFromChars(NekDouble &u, const NekDouble &W1,
103 const NekDouble &W2)
104{
105 u = (W1 + W2) / 2; // Necessarily the case for all tube laws
106}
107
108void BetaPressureArea::v_GetCharIntegral(
109 NekDouble &I, const NekDouble &beta, const NekDouble &A,
110 const NekDouble &A0, [[maybe_unused]] const NekDouble &alpha)
111{
112 NekDouble c = 0.0;
113 NekDouble c0 = 0.0;
114
115 GetC(c, beta, A, A0);
116 GetC(c0, beta, A0, A0);
117
118 I = 4 * (c - c0);
119}
120
121void BetaPressureArea::v_GetJacobianInverse(NekMatrix<NekDouble> &invJ,
122 const Array<OneD, NekDouble> &Au,
123 const Array<OneD, NekDouble> &uu,
124 const Array<OneD, NekDouble> &beta,
125 const Array<OneD, NekDouble> &A0,
126 const Array<OneD, NekDouble> &alpha,
127 const std::string &type)
128{
129 /*
130 In the interest of speed, the inverse of the Jacobians for bifurcations,
131 merges and junctions for the beta law have been calculated analytically.
132 This can be done for other laws too, or the general formulation can be used
133 instead.
134 */
135
136 NekDouble k = 0.0;
137
138 if (type == "Bifurcation")
139 {
140 NekMatrix<NekDouble> J(6, 6);
141 Array<OneD, NekDouble> c(3);
142 Array<OneD, NekDouble> K(3);
143
144 for (int i = 0; i < 3; ++i)
145 {
146 GetC(c[i], beta[i], Au[i], A0[i], alpha[i]);
147 }
148
149 k = c[0] * Au[1] * c[2] + Au[0] * c[2] * c[1] + Au[2] * c[0] * c[1];
150 K[0] = (c[0] - uu[0]) * k;
151 K[1] = (c[1] + uu[1]) * k;
152 K[2] = (c[2] + uu[2]) * k;
153
154 invJ.SetValue(0, 0,
155 (-c[1] * uu[0] * c[2] * Au[0] +
156 Au[2] * c[1] * c[0] * c[0] +
157 Au[1] * c[0] * c[0] * c[2]) /
158 K[0]);
159 invJ.SetValue(0, 1, Au[1] * (c[1] - uu[1]) * c[0] * c[2] / K[0]);
160 invJ.SetValue(0, 2, Au[2] * (c[2] - uu[2]) * c[0] * c[1] / K[0]);
161 invJ.SetValue(0, 3, c[0] * c[1] * c[2] / K[0]);
162 invJ.SetValue(0, 4, -0.5 * c[0] * Au[1] * c[2] / K[0]);
163 invJ.SetValue(0, 5, -0.5 * Au[2] * c[0] * c[1] / K[0]);
164
165 invJ.SetValue(1, 0, Au[0] * (c[0] + uu[0]) * c[1] * c[2] / K[1]);
166 invJ.SetValue(1, 1,
167 (c[0] * uu[1] * c[2] * Au[1] +
168 Au[2] * c[0] * c[1] * c[1] +
169 c[2] * c[1] * c[1] * Au[0]) /
170 K[1]);
171 invJ.SetValue(1, 2, -Au[2] * (c[2] - uu[2]) * c[0] * c[1] / K[1]);
172 invJ.SetValue(1, 3, -c[0] * c[1] * c[2] / K[1]);
173 invJ.SetValue(1, 4, -0.5 * (c[0] * Au[2] + Au[0] * c[2]) * c[1] / K[1]);
174 invJ.SetValue(1, 5, 0.5 * Au[2] * c[0] * c[1] / K[1]);
175
176 invJ.SetValue(2, 0, Au[0] * (c[0] + uu[0]) * c[1] * c[2] / K[2]);
177 invJ.SetValue(2, 1, -Au[1] * (c[1] - uu[1]) * c[0] * c[2] / K[2]);
178 invJ.SetValue(2, 2,
179 (c[0] * c[1] * uu[2] * Au[2] +
180 c[0] * Au[1] * c[2] * c[2] +
181 c[1] * c[2] * c[2] * Au[0]) /
182 K[2]);
183 invJ.SetValue(2, 3, -c[0] * c[1] * c[2] / K[2]);
184 invJ.SetValue(2, 4, 0.5 * c[0] * Au[1] * c[2] / K[2]);
185 invJ.SetValue(2, 5, -0.5 * (Au[1] * c[0] + c[1] * Au[0]) * c[2] / K[2]);
186
187 invJ.SetValue(3, 0,
188 Au[0] *
189 (Au[0] * c[2] * c[1] - uu[0] * c[2] * Au[1] -
190 uu[0] * c[1] * Au[2]) /
191 K[0]);
192 invJ.SetValue(3, 1, -Au[0] * Au[1] * (c[1] - uu[1]) * c[2] / K[0]);
193 invJ.SetValue(3, 2, -Au[0] * Au[2] * (c[2] - uu[2]) * c[1] / K[0]);
194 invJ.SetValue(3, 3, -Au[0] * c[2] * c[1] / K[0]);
195 invJ.SetValue(3, 4, 0.5 * Au[0] * Au[1] * c[2] / K[0]);
196 invJ.SetValue(3, 5, 0.5 * Au[0] * c[1] * Au[2] / K[0]);
197
198 invJ.SetValue(4, 0, Au[0] * Au[1] * (c[0] + uu[0]) * c[2] / K[1]);
199 invJ.SetValue(4, 1,
200 -Au[1] *
201 (c[0] * Au[1] * c[2] + c[0] * uu[1] * Au[2] +
202 c[2] * uu[1] * Au[0]) /
203 K[1]);
204 invJ.SetValue(4, 2, -Au[2] * Au[1] * (c[2] - uu[2]) * c[0] / K[1]);
205 invJ.SetValue(4, 3, -c[0] * Au[1] * c[2] / K[1]);
206 invJ.SetValue(4, 4,
207 -0.5 * Au[1] * (c[0] * Au[2] + Au[0] * c[2]) / K[1]);
208 invJ.SetValue(4, 5, 0.5 * Au[2] * Au[1] * c[0] / K[1]);
209
210 invJ.SetValue(5, 0, Au[0] * Au[2] * (c[0] + uu[0]) * c[1] / K[2]);
211 invJ.SetValue(5, 1, -Au[2] * Au[1] * (c[1] - uu[1]) * c[0] / K[2]);
212 invJ.SetValue(5, 2,
213 -Au[2] *
214 (Au[2] * c[0] * c[1] + c[0] * uu[2] * Au[1] +
215 c[1] * uu[2] * Au[0]) /
216 K[2]);
217 invJ.SetValue(5, 3, -Au[2] * c[0] * c[1] / K[2]);
218 invJ.SetValue(5, 4, 0.5 * Au[2] * Au[1] * c[0] / K[2]);
219 invJ.SetValue(5, 5,
220 -0.5 * Au[2] * (Au[1] * c[0] + c[1] * Au[0]) / K[2]);
221 }
222 else if (type == "Merge")
223 {
224 NekMatrix<NekDouble> J(6, 6);
225 Array<OneD, NekDouble> c(3);
226 Array<OneD, NekDouble> K(3);
227
228 for (int i = 0; i < 3; ++i)
229 {
230 GetC(c[i], beta[i], Au[i], A0[i], alpha[i]);
231 }
232
233 k = c[0] * Au[1] * c[2] + Au[0] * c[2] * c[1] + Au[2] * c[0] * c[1];
234 K[0] = (c[0] - uu[0]) * k;
235 K[1] = (c[1] + uu[1]) * k;
236 K[2] = (c[2] + uu[2]) * k;
237
238 invJ.SetValue(0, 0,
239 (-c[1] * uu[0] * c[2] * Au[0] +
240 Au[2] * c[1] * c[0] * c[0] +
241 Au[1] * c[0] * c[0] * c[2]) /
242 K[0]);
243 invJ.SetValue(0, 1, Au[1] * (c[1] - uu[1]) * c[0] * c[2] / K[0]);
244 invJ.SetValue(0, 2, Au[2] * (c[2] - uu[2]) * c[0] * c[1] / K[0]);
245 invJ.SetValue(0, 3, c[0] * c[1] * c[2] / K[0]);
246 invJ.SetValue(0, 4, -0.5 * c[0] * Au[1] * c[2] / K[0]);
247 invJ.SetValue(0, 5, -0.5 * Au[2] * c[0] * c[1] / K[0]);
248
249 invJ.SetValue(1, 0, Au[0] * (c[0] + uu[0]) * c[1] * c[2] / K[1]);
250 invJ.SetValue(1, 1,
251 (c[0] * uu[1] * c[2] * Au[1] +
252 Au[2] * c[0] * c[1] * c[1] +
253 c[2] * c[1] * c[1] * Au[0]) /
254 K[1]);
255 invJ.SetValue(1, 2, -Au[2] * (c[2] - uu[2]) * c[0] * c[1] / K[1]);
256 invJ.SetValue(1, 3, -c[0] * c[1] * c[2] / K[1]);
257 invJ.SetValue(1, 4, -0.5 * (c[0] * Au[2] + Au[0] * c[2]) * c[1] / K[1]);
258 invJ.SetValue(1, 5, 0.5 * Au[2] * c[0] * c[1] / K[1]);
259
260 invJ.SetValue(2, 0, Au[0] * (c[0] - uu[0]) * c[1] * c[2] / K[2]);
261 invJ.SetValue(2, 1, -Au[1] * (c[1] + uu[1]) * c[0] * c[2] / K[2]);
262 invJ.SetValue(2, 2,
263 -(c[0] * uu[2] * c[1] * Au[2] -
264 Au[1] * c[0] * c[2] * c[2] -
265 c[1] * c[2] * c[2] * Au[0]) /
266 K[2]);
267 invJ.SetValue(2, 3, -c[0] * c[1] * c[2] / K[2]);
268 invJ.SetValue(2, 4, -0.5 * Au[1] * c[0] * c[2] / K[2]);
269 invJ.SetValue(2, 5, 0.5 * (Au[1] * c[0] + Au[0] * c[1]) * c[2] / K[2]);
270
271 invJ.SetValue(3, 0,
272 -Au[0] *
273 (Au[0] * c[2] * c[1] + uu[0] * c[2] * Au[1] +
274 uu[0] * c[1] * Au[2]) /
275 K[0]);
276 invJ.SetValue(3, 1, Au[0] * Au[1] * (c[1] + uu[1]) * c[2] / K[0]);
277
278 invJ.SetValue(3, 2, -Au[0] * Au[2] * (c[2] - uu[2]) * c[1] / K[0]);
279 invJ.SetValue(3, 3, -Au[0] * c[2] * c[1] / K[0]);
280 invJ.SetValue(3, 4, 0.5 * Au[0] * Au[1] * c[2] / K[0]);
281 invJ.SetValue(3, 5, 0.5 * Au[0] * c[1] * Au[2] / K[0]);
282
283 invJ.SetValue(4, 0, Au[0] * Au[1] * (c[0] + uu[0]) * c[2] / K[1]);
284 invJ.SetValue(4, 1,
285 -Au[1] *
286 (c[0] * Au[1] * c[2] + c[0] * uu[1] * Au[2] +
287 c[2] * uu[1] * Au[0]) /
288 K[1]);
289 invJ.SetValue(4, 2, -Au[2] * Au[1] * (c[2] - uu[2]) * c[0] / K[1]);
290 invJ.SetValue(4, 3, -c[0] * Au[1] * c[2] / K[1]);
291 invJ.SetValue(4, 4,
292 -0.5 * Au[1] * (c[0] * Au[2] + Au[0] * c[2]) / K[1]);
293 invJ.SetValue(4, 5, 0.5 * Au[2] * Au[1] * c[0] / K[1]);
294
295 invJ.SetValue(5, 0, Au[0] * Au[2] * (c[0] + uu[0]) * c[1] / K[2]);
296 invJ.SetValue(5, 1, -Au[2] * Au[1] * (c[1] - uu[1]) * c[0] / K[2]);
297 invJ.SetValue(5, 2,
298 -Au[2] *
299 (Au[2] * c[0] * c[1] + c[0] * uu[2] * Au[1] +
300 c[1] * uu[2] * Au[0]) /
301 K[2]);
302 invJ.SetValue(5, 3, -Au[2] * c[0] * c[1] / K[2]);
303 invJ.SetValue(5, 4, 0.5 * Au[2] * Au[1] * c[0] / K[2]);
304 invJ.SetValue(5, 5,
305 -0.5 * Au[2] * (Au[1] * c[0] + c[1] * Au[0]) / K[2]);
306 }
307 else if (type == "Interface")
308 {
309 NekMatrix<NekDouble> J(4, 4);
310 Array<OneD, NekDouble> c(2);
311 Array<OneD, NekDouble> K(2);
312
313 for (int i = 0; i < 2; ++i)
314 {
315 GetC(c[i], beta[i], Au[i], A0[i], alpha[i]);
316 }
317
318 k = (c[0] * Au[1] + Au[0] * c[1]);
319 K[0] = (c[0] + uu[0]) * k;
320 K[1] = (c[1] + uu[1]) * k;
321
322 invJ.SetValue(0, 0,
323 (Au[1] * c[0] * c[0] - c[1] * uu[0] * Au[0]) / K[0]);
324 invJ.SetValue(0, 1, Au[1] * (c[1] - uu[1]) * c[0] / K[0]);
325 invJ.SetValue(0, 2, c[0] * c[1] / K[0]);
326 invJ.SetValue(0, 3, -0.5 * c[0] * Au[1] / K[0]);
327
328 invJ.SetValue(1, 0, Au[0] * (c[0] + uu[0]) * c[1] / K[1]);
329 invJ.SetValue(1, 1,
330 (c[0] * uu[1] * Au[1] + c[1] * c[1] * Au[0]) / K[1]);
331 invJ.SetValue(1, 2, -c[0] * c[1] / K[1]);
332 invJ.SetValue(1, 3, -0.5 * Au[0] * c[1] / K[1]);
333
334 invJ.SetValue(2, 0, Au[0] * (Au[0] * c[1] - uu[0] * Au[1]) / K[0]);
335 invJ.SetValue(2, 1, -Au[0] * Au[1] * (c[1] - uu[1]) / K[0]);
336 invJ.SetValue(2, 2, -Au[0] * c[1] / K[0]);
337 invJ.SetValue(2, 3, 0.5 * Au[1] * Au[0] / K[0]);
338
339 invJ.SetValue(3, 0, Au[0] * Au[1] * (c[0] + uu[0]) / K[1]);
340 invJ.SetValue(3, 1, -Au[1] * (c[0] * Au[1] + uu[1] * Au[0]) / K[1]);
341 invJ.SetValue(3, 2, -c[0] * Au[1] / K[1]);
342 invJ.SetValue(3, 3, -0.5 * Au[1] * Au[0] / K[1]);
343 }
344}
345
346} // namespace Nektar
Nektar::BetaPressureArea::BetaPressureArea
BetaPressureArea(Array< OneD, MultiRegions::ExpListSharedPtr > pVessel, const LibUtilities::SessionReaderSharedPtr pSession)
Definition: BetaPressureArea.cpp:46
Nektar::BetaPressureArea::v_GetPressure
void v_GetPressure(NekDouble &P, const NekDouble &beta, const NekDouble &A, const NekDouble &A0, const NekDouble &dAUdx, const NekDouble &gamma=0, const NekDouble &alpha=0.5) override
Definition: BetaPressureArea.cpp:53
Nektar::BetaPressureArea::v_GetCharIntegral
void v_GetCharIntegral(NekDouble &I, const NekDouble &beta, const NekDouble &A, const NekDouble &A0, const NekDouble &alpha=0.5) override
Definition: BetaPressureArea.cpp:108
Nektar::BetaPressureArea::create
static PulseWavePressureAreaSharedPtr create(Array< OneD, MultiRegions::ExpListSharedPtr > &pVessel, const LibUtilities::SessionReaderSharedPtr &pSession)
Definition: BetaPressureArea.h:55
Nektar::BetaPressureArea::className
static std::string className
Definition: BetaPressureArea.h:63
Nektar::BetaPressureArea::v_GetW2
void v_GetW2(NekDouble &W2, const NekDouble &u, const NekDouble &beta, const NekDouble &A, const NekDouble &A0, const NekDouble &alpha=0.5) override
Definition: BetaPressureArea.cpp:82
Nektar::BetaPressureArea::v_GetUFromChars
void v_GetUFromChars(NekDouble &u, const NekDouble &W1, const NekDouble &W2) override
Definition: BetaPressureArea.cpp:102
Nektar::BetaPressureArea::v_GetC
void v_GetC(NekDouble &c, const NekDouble &beta, const NekDouble &A, const NekDouble &A0, const NekDouble &alpha=0.5) override
Definition: BetaPressureArea.cpp:63
Nektar::BetaPressureArea::v_GetJacobianInverse
void v_GetJacobianInverse(NekMatrix< NekDouble > &invJ, const Array< OneD, NekDouble > &Au, const Array< OneD, NekDouble > &uu, const Array< OneD, NekDouble > &beta, const Array< OneD, NekDouble > &A0, const Array< OneD, NekDouble > &alpha, const std::string &type) override
Definition: BetaPressureArea.cpp:121
Nektar::BetaPressureArea::v_GetW1
void v_GetW1(NekDouble &W1, const NekDouble &u, const NekDouble &beta, const NekDouble &A, const NekDouble &A0, const NekDouble &alpha=0.5) override
Definition: BetaPressureArea.cpp:71
Nektar::BetaPressureArea::v_GetAFromChars
void v_GetAFromChars(NekDouble &A, const NekDouble &W1, const NekDouble &W2, const NekDouble &beta, const NekDouble &A0, const NekDouble &alpha=0.5) override
Definition: BetaPressureArea.cpp:93
Nektar::LibUtilities::NekFactory::RegisterCreatorFunction
tKey RegisterCreatorFunction(tKey idKey, CreatorFunction classCreator, std::string pDesc="")
Register a class with the factory.
Definition: BasicUtils/NekFactory.hpp:197
Nektar::PulseWavePressureArea::GetCharIntegral
void GetCharIntegral(NekDouble &I, const NekDouble &beta, const NekDouble &A, const NekDouble &A0, const NekDouble &alpha=0.5)
Definition: PulseWavePressureArea.h:108
Nektar::PulseWavePressureArea::GetC
void GetC(NekDouble &c, const NekDouble &beta, const NekDouble &A, const NekDouble &A0, const NekDouble &alpha=0.5)
Definition: PulseWavePressureArea.h:75
Nektar::LibUtilities::SessionReaderSharedPtr
std::shared_ptr< SessionReader > SessionReaderSharedPtr
Definition: SessionReader.h:119
Nektar::LibUtilities::beta
@ beta
Gauss Radau pinned at x=-1,.
Definition: PointsType.h:59
Nektar::LibUtilities::P
@ P
Monomial polynomials .
Definition: BasisType.h:62
Nektar::GetPressureAreaFactory
PressureAreaFactory & GetPressureAreaFactory()
Definition: PulseWavePressureArea.cpp:50
Nektar::NekDouble
double NekDouble
Definition: NektarUnivTypeDefs.hpp:43
tinysimd::sqrt
scalarT< T > sqrt(scalarT< T > in)
Definition: scalar.hpp:285
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